How can I make a track for an object in Blender Game (not blender render)?
You can use the Edit Object Actuator and set it to "Track to". Set the Object you want to track to in the Object Picker and choose the track axis. If you pick x it will point with the x axis to the object to track etc. If you want the object to rotate only around the z axis, don't enable 3d. If you want every axis, enable 3d. UP axis should usually stay z if you didn't rotate your object in a strange way (it means z will point up).


Suzanne tracks to the cube on the y axis


with 3D enabled she also lifts her head for it.